Apple Pencil warranty

Depends on the type/cause of damage it will be determined to be. If your dog chewed it, then it wouldn't be - if it is a mfr's problem, then it would be.

Take it to your nearest store and have it examined; bring along your receipt.

If the [relatively] fragile metal transducer that interacts with the iPad screen (the transducer being located beneath the user-replaceable pencil tip) has been damaged, your Pencil may not work at all. Your one-year limited warranty covers manufacturing and material defects only; it does not cover accidental damage of any kind. If the Pencil has been dropped onto its tip, the transducer is easily damaged.

If the Pencil was purchased at the same time as your iPad, should you have taken the opportunity purchase the optional AppleCare+ plan for your iPad, then your Pencil would also benefit from accidental damage coverage afforded by AppleCare+.

A damaged Apple Pencil cannot be repaired - only replaced.

The technicians at your local Apple Store or Apple Authorised Service Provider (AASP) will be best able to test and assess your Pencil. With benefit of assessment, you’ll be in the best possible place to explore your available options:

Genius Bar Reservation and Apple Support Options - Apple

you can read about their warranty here Legal - Hardware Warranties - Apple